login
A176669
A triangle of polynomial coefficients:p(x,n)=Sum[(2*k - 1)^n*Binomial[x, k], {k, 0, Infinity}]/2^x
0
1, -1, 1, 1, -1, 1, -1, 0, 0, 1, 1, 0, -3, 2, 1, -1, 5, -5, -5, 5, 1, 1, -5, 30, -35, 0, 9, 1, -1, -56, 91, 35, -105, 21, 14, 1, 1, 56, -518, 812, -245, -196, 70, 20, 1, -1, 1329, -2610, -42, 2793, -1449, -210, 162, 27, 1, 1, -1329, 15075, -28110, 14385, 4053, -4515, 90
OFFSET
0,13
COMMENTS
Row sums are:
{1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1,...}.
FORMULA
p(x,n)=Sum[(2*k - 1)^n*Binomial[x, k], {k, 0, Infinity}]/2^x;
t(n,m)=coefficients(p(x,n))
EXAMPLE
{1},
{-1, 1},
{1, -1, 1},
{-1, 0, 0, 1},
{1, 0, -3, 2, 1},
{-1, 5, -5, -5, 5, 1},
{1, -5, 30, -35, 0, 9, 1},
{-1, -56, 91, 35, -105, 21, 14, 1},
{1, 56, -518, 812, -245, -196, 70, 20, 1},
{-1, 1329, -2610, -42, 2793, -1449, -210, 162, 27, 1},
{1, -1329, 15075, -28110, 14385, 4053, -4515, 90, 315, 35, 1}
MATHEMATICA
Clear[p, x, n]
p[x_, n_] = Sum[(2*k - 1)^n*Binomial[x, k], {k, 0, Infinity}]/2^x;
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}];
Flatten[%]
CROSSREFS
Sequence in context: A269233 A123396 A225800 * A327615 A058280 A113185
KEYWORD
sign,tabl,uned
AUTHOR
Roger L. Bagula, Apr 23 2010
STATUS
approved